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Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                    Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                     Vol. 3, Issue 1, January -February 2013, pp1306-1312
  Offset-Strip Fin Heat Exchangers A Conceptual Review Study
                        ALOK VYAS *, Dr. Alka Bani Agrawal **
   *(Department of Mechanical Engineering, Rajeev Gandhi Proudyogiki Vishwavidyalaya, Bhopal (M.P.) –
                                                462038)
  **(Department of Mechanical Engineering, Rajeev Gandhi Proudyogiki Vishwavidyalaya, Bhopal (M.P.) –
                                                462038)

Abstract
         This paper is a review of research work         The geometry of the offset strip fin surface is
of last few years on heat transfer growth in             described by the following parameters:
offset-strip fin heat exchangers. It features a          (i) Fin spacing (s), excluding the fin thickness,
broad discussion on the application of enhanced          (ii) Fin height (h), excluding the fin thickness,
heat transfer surfaces to offset strip fin heat          (iii) Fin thickness (t), and
exchangers. In this paper we are discussing 2D           (iv) The strip length (_), in the flow direction.
& 3D Analysis in OSF, Experimental &                                The lateral fin offset is generally uniform
investigating research on OSFs, Analytical model         and equal to half the fin spacing (including fin
to predict the heat transfer coefficient and the         thickness). Figure shows a schematic view of the
friction factor of the OSFs geometry, Heat               rectangular offset strip fin surface and defines the
transfer and pressure drop Characteristics of an         geometric parameters. The following are some
OSFs Thermal performance, CFD Analysis on                commonly used secondary parameters derived from
OSFs.                                                    the basic fin dimensions

Keywords - CFD Analysis, Offset-strip fin, Heat
transfer growth, laminar and turbulent flow.

INTRODUCTION
          The first sign of movement to relatively
“compact” heat exchangers was seen in the
automotive industry in the early 1900’s, when an
improved manner for removing heat from engines
with minimal material (weight) was sought.
Whereas heat was previously removed from engines
by boiling a collection of water and releasing it into   Fig.1Offset-strip fin Geometry
the air in an unsophisticated convection process,
heat exchangers were seen as an inexpensive way to
improve engine performance (Shah & Sekulic,
                                                         1. Two & Three Dimensional analysis in
2003).[1]                                                OSFs Heat Exchangers
          The offset strip fin is one of the most                  Patankar and Prakash [2] presented a two
widely used finned surfaces, particularly in high        dimensional analysis for the flow and heat transfer
effectiveness heat exchangers employed in                in an interrupted plate passage which is an
cryogenic and aircraft applications. These fins are      idealization of the OSFs heat exchanger. The main
created by cutting a set of plain rectangular fins       aim of the study is investigating the effect of plate
periodically along the flow direction, and shifting      thickness in a non-dimensional form t/H on heat
each strip thus generated by half the fin spacing        transfer and pressure drop in OSF channels because
alternately left and rightward.                          the impingement region resulting from thick plate
          The flow is thus periodically interrupted,     on the leading edge and recalculating region behind
leading to creation of fresh boundary layers and         the trailing edge are absent if the plate thickness is
consequent heat transfer improvement. Interruption       neglected. Their calculation method was based on
of flow also leads to greater viscous pressure drop,     the periodically fully developed flow through one
manifested by a higher value of effective friction       periodic module since the flow in OSF channels
factor. In addition to the effect of wall shear,         attains a periodic fully developed behaviour after a
resistance to flow also increases due to form drag       short entrance region, which may extend to about 5
over the leading edges of the fin sections facing the    (at the most 10) ranks of plates (Sparrow, et al.
flow, and due to trailing edge vortices. The effective   1977). Steady and laminar flow was assumed by
heat transfer coefficient and friction factor are        them between Reynolds numbers 100 to 2000. They
composite effects of the above mechanisms.               found the flow to be mainly laminar in this range,
The Offset Strip Fin Geometry                            although in some cases just before the Reynolds no.
                                                         2000 there was a transition from laminar to



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Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                    Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                     Vol. 3, Issue 1, January -February 2013, pp1306-1312
turbulence. Specially for the higher values of t/H.       from 10 to 2000 in both the papers. The results of
They used the constant heat flow boundary                 the two studies showed that the Prandtl number has
condition with each row of fins at fixed temperature.     a significant effect on heat transfer in OSF
They made their analysis for different fin thickness      channel.Although there is no effect on the pressure
ratios t/H= 0, 0.1, 0.2, 0.3 for the same fin length      drop.
L/H = 1, and they fixed the Prandtl number of fluid                 Zhang et al [7] investigated the
= 0.7. For proper validation they compared there          mechanisms for heat transfer enhancement in
numerical results with the experimental results of        parallel plate fin heat exchangers including the
[London and Shah][1] for offset strip fin heat            inline and staggered arrays of OSFs. They have also
exchangers. The result indicated reasonable               taken into account the effect of fin thickness and the
agreement for the f factors, but the predicted j factor   time dependent flow behavior due to the vortex
was twice as large as the experimental data. They         shedding by solving the unsteady momentum and
concluded that the thick plate situation leads to         energy equation. The effects of vortices which are
significantly higher pressure drop while the heat         generated at the leading edge of the fins and travel
transfer does not sufficiently improve despite the        downstream along the fin surface was also studied.
increased surface area and increased mean velocity.       From there study they found that only the surface
 Fangjun Hong & Ping Cheng [3] show the 3-D               interruptions increase the heat transfer because they
numerical simulation, taking into consideration the       cause the boundary layers to start periodically on fin
conjugate heat transfer of heat sink base material        surfaces and reduce the thermal resistance to
and coolant, was conducted for laminar forced             transfer heat between the fin surfaces and fluid.
convection of water to study offset strip fin micro       However after a critical Reynolds number the flow
channel heat sink for microelectronic cooling. It is      becomes unsteady and in this regime the vortices
found that due to the periodical change of the flow       play a major role to increase the heat transfer by
direction, the convective heat transfer is enhanced       bringing the fresh fluids continuously from the main
by mixing the cold and hot coolant, and the               stream towards the fin surface.
periodical breakup of boundary layer is another                     Dejong et al [8] carried out an experimental
factor to enhance heat transfer. The effects of the       and numerical study for understanding the flow and
ratio of fin interval to fin length K, and fin numbers    heat transfer in OSFs. In the study the pressure drop,
M on the performance of strip-fin micro channel           local Nusselt number, average heat transfer and skin
were also investigated. It is found that for the same     friction coefficient on fin surface, instantaneous
K, with the increase of M, the required mass flow         flow structures and local time averaged velocity
rate to keep the maximum wall temperature                 profiles in OSF channel were investigated. They
decreases.                                                compared there results with the experimental results
                                                          obtained by Dejong and Jacobi [1997] and unsteady
2. Experimental & investigating research on               numerical simulation of Zhang et al [1997]. There
OSFs                                                      results indicate that the boundary layer
          Manglik and Bergles[4] carried an               development, flow separation and reattachment,
experimental research on OSFs. They investigated          wake formation and vortex shedding play an
the effects of fin geometries as non dimensional          important role in the OSF geometry.
forms on heat transfer and pressure drop, for their        S.YoucefAli_,J.Y.Desmons[9] Presented
study they used 18 different OSFs. After their                      A mathematical model that allows the
analysis they arrived upon two correlations, one for      determination of the thermal performances of the
heat transfer and another one for pressure drop. The      single pass solar air collector with offset rectangular
correlations were developed for all the three regions.    plate fin absorber plate is developed (fig.2). The
They compared there results from the data obtained        model can predict the temperature profile of all the
by other researchers in the deep laminar and fully        components of the collector and of the air stream in
turbulent regions. There correlations can be              the channel duct.the offset rectangular plate fins
acceptable when comparing the results of the              were introduced, which increase the thermal heat
expressions to the experimental data obtained by          transfer between the absorber plate and the fluid.
Kays and London [5].                                      The offset rectangular plate fins, mounted in a
          Hu and Herold [6] presented two papers to       staggered pattern, are oriented parallel to the fluid
show the effect of Prandtl no. on heat transfer and       flow and are soldered to the underside of the
pressure drop in OSF array. Experimental study was        absorber plate. They are characterized by high heat
carried out in the first paper to study the effect for    transfer area per unit volume and generate the low
which they used the seven OSFs having different           pressure losses. The experimental results of the air
geometries and three working fluids with different        stream temperature will be compared with the
Prandtl number. At the same time the effect of
changing the Prandtl number of fluid with
temperature was also investigated. The study was
carried out in the range of Reynolds number varying


                                                                                                1307 | P a g e
Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                    Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                     Vol. 3, Issue 1, January -February 2013, pp1306-1312
results obtained by the theoretical model suggested




                                                          Fig.3(a) Laminar flow on the fins and in the wakes
Fig. 2 Experimental setup                                 (Source Joshi and Webb 1987)
The model, which determines the thermal
performances of this collector and temperatures of
all its components and air stream, uses an equation
of global irradiance incident along the collector,
ambient and inlet collector temperature. Predicted
and experimental results of the air stream
temperature are in good agreement particularly in
the transition flow regime. On the other hand, in the
laminar flow system, the greatest recorded variation,
which is of 71ↄC obtained for the lowest value of
the Reynolds number Re ¼ 479. In this same case,
the difference between the theoretical and the
experimental air stream temperature at the collector      Fig.3(b) Laminar flow on the fins and oscillating
exit is only of 41 ↄC which is acceptable.                flow on the wakes
                                                          (Source Joshi and Webb 1987)
3. Analytical model to predict the heat
transfer coefficient and the friction factor of                     Four different flow regimes were identified
the OSFs geometry                                         by Joshi and Webb [12] from their experiment. The
          Joshi and Webb [10] developed an                flow was found to be laminar and steady in the first
analytical model to predict the heat transfer             regime. In the second regime the oscillating flow
coefficient and the friction factor of the offset strip   structures were found in the transverse direction.
fin surface geometry. To study the transition from        The flow oscillated in the wake region between two
laminar to turbulent flow they conducted the flow         successive fins in the third regime. And in the fourth
visualization experiments and an equation based on        regime the effect of vortex shedding came into
the conditions in wake was developed. They also           picture. The laminar flow correlation of Joshi and
modified the correlations of Weiting [11]. There          Webb started to under predict the j and f factors at
was some difference between there correlation. Four       the second regime. So they assumed the Reynolds
different flow regimes were identified by Joshi and       number at that point as the critical Reynolds number
Webb [12] from there experiment. The flow was             to identify the transition from laminar to turbulent.
found to be laminar and steady in the first regime. In
the second regime the oscillating flow structures         4. Heat transfer and pressure                   drop
were found in the transverse direction. The flow          Characteristics of an OSFs
oscillated in the wake region between two                          H. Bhowmik and Kwan-Soo Lee [13]
successive fins in the third regime. And in the fourth    studied the heat transfer and pressure drop
regime the effect of vortex shedding came into            characteristics of an offset strip fin heat exchanger.
picture. The laminar flow correlation of Joshi and        For their study they used a steady state three
Webb started to under predict the j and f factors at      dimensional numerical model. They have took water
the second regime. So they assumed the Reynolds           as the heat transfer medium, and the Reynolds
number at that point as the critical Reynolds number      number (Re)in the range of 10 to 3500. Variations in
to identify the transition from laminar to turbulent.     the Fanning friction factor f and the Colburn heat
                                                          transfer j relative to Reynolds number were
                                                          observed. General correlations for the f and j factors
                                                          were derived by them which could be used to
                                                          analyze fluid flow and heat transfer Characteristics
                                                          of offset strip fins in the laminar, transition, and
                                                          turbulent regions of the flow.


                                                                                               1308 | P a g e
Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                              Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                               Vol. 3, Issue 1, January -February 2013, pp1306-1312
                                                                 heat transfer coefficient. They also derived the j
                                                                 factor and f factor by using regression analysis.
                                                                 Results showed that the heat transfer coefficient and
                                                                 pressure drop reduce with enlarging the fin space,
                                                                 fin height and fin length.
                                                                           Michna et al [16] investigated the effect of
                                                                 increasing Reynolds number on the performance of
                                                                 OSFs. He conducted the experiment at Reynolds
                                                                 number between 5000 to 120000 and found that
                                                                 both heat transfer and pressure drop increased with
                                                                 increasing Reynolds number, because the effect of
                                                                 vortex shedding and eddy formation at turbulent
                                                                 regime. Operation of OSF heat exchangers under
         Fig.4 Direction of fluid at LPD & HPD                   this Reynolds number may be useful in systems
                                                                 where minimizing the heat exchanger size or
                  Saidi and Sudden [14] carried out a            maximizing the heat transfer coefficient is more
         numerical analysis of the instantaneous flow and        important than minimizing the pressure drop.
         heat transfer for OSF geometries in self-sustained                Various experiments are carried out in
         time-dependent oscillatory flow. The effect of          order to find out the j and f factors of the various
         vortices over the fin surfaces on heat transfer was     heat exchangers and are called as the thermal
         studied at intermediate Reynolds numbers where the      performance testing. These testing are needed for
         flow remains laminar, but unsteadiness and vortex       heat exchangers, which do not have reported j and f
         shedding tends to dominate. They compared their         data. Therefore, this test is conducted for any new
         numerical results with previous numerical and           development or modification of the finned surfaces.
         experimental data done by Dejong, et al. (1998).        T. Lestina & K. Bell, Advances in Heat Transfer,
                                                                 told for heat exchangers already existing in the
                                                                 plants this test is done for the following reasons:
                                                                 a) Comparison of the measured performance with
                                                                 specification or manufacturing design rating data.
                                                                 b) Evaluation of the cause of degradation or
                                                                 malfunctioning.
                                                                 c) Assessment of process improvements such as
                                                                 those due to enhancement or heat exchanger
                                                                 replacement.
                                                                           Another reason for developing these
                                                                 correlations is that, generally in most heat exchanger
                                                                 problems the working fluid, the heat flow rate and
Fig. 5. Heat transfer in offset plate fins                       mass flow rate are usually known, so if certain
                                                                 correlations between geometry and fin performance
                   The studies of few researchers like           is also known, then the problem can be deeply
         Patankar and Prakash [1], Kays and London [5] it is     simplified. For that purpose developing the
         easy to get information regarding the effects of        correlations for fanning friction factor f and
         OSFs on heat transfer and pressure drop. But most       Colbourn factor j are important for heat
         of the researchers have not taken into account the      exchanger.These are the ratio of free flow area (
         effect of manufacturing irregularities such as burred   = s/h), the ratio of heat transfer area (β= t/l), and the
         edges, bonding imperfections, separating plate          ratio of fin density (y= t/s).
         roughness which also affect the heat transfer and       Show in Fig.1
         flow friction characteristics of the heat exchanger.
         Dong et al [15] made experiments and analysis           5. Thermal performance of OSF Heat
         considering the above factors to get better thermal
                                                                 Exchangers
         and hydraulic performance from the OSFs. Sixteen
                                                                           S. Youcef-Ali_, J.Y. Desmons [17] A
         types of OSFs and flat tube heat exchangers were
                                                                 mathematical model that allows the determination of
         used to make the experimental studies on heat
                                                                 the thermal performances of the single pass solar air
         transfer and pressure drop characteristics. A number
                                                                 collector with offset rectangular plate fin absorber
         of tests were made by changing the various fin
                                                                 plate is developed. The model, which determines the
         parameters and all the tests were carried out in
                                                                 thermal performances of this collector and
         specific region of air side Reynolds number (500-
                                                                 temperatures of all its components and air stream,
         7500), at a constant water flow crate. The thermal
                                                                 uses an equation of global irradiance incident along
         performance data was analyzed using the
                                                                 the collector, ambient and inlet collector
         effectiveness-NTU method in order to obtain the


                                                                                                        1309 | P a g e
Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                    Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                     Vol. 3, Issue 1, January -February 2013, pp1306-1312
temperature. Predicted and experimental results of        railway industry (Shah, McDonald, & Howard,
the air stream temperature are in good agreement          1980).[21] The 1980’s brought an increase in
particularly in the transition flow regime.               computing power and function that led compact heat
                                                          exchanger research away from experimental
          Suzuki et al [18] in order to study the         solutions in favor of Computational Fluid Dynamics
thermal performance of a staggered array of vertical      (CFD). CFD provided low-cost means to simulate
flat plates at low Reynolds number has taken a            the physics occurring inside heat exchangers
different numerical approach by solving the elliptic      relatively accurately, without the need to construct
differential equations governing the flow of              and test physical apparatus before a final design was
momentum and energy. The validation of their              developed.
numerical model has been done by carrying out
experiments on a two dimensional system, followed
by those on a practical offset strip fin heat
exchanger. The experimental result was in good
agreement with the performance study for the
practical offset-strip-fin type heat exchanger in the
range of Reynolds number of Re<800.
          Tinaut et al [19] developed two correlations
for heat transfer and flow friction coefficients for
OSFs and plane parallel plates. The working fluid
for OSF was engine oil and water was taken for
analyzing the parallel plate channels. By using the
correlations of Dittus and Boelter and some
expressions of Kays and Crawford they obtained
their correlations. For the validation of their results
they compared there correlations with correlations
of                                         Weitng[6].     Fig. 6. CFD Analysis in offset plate fins
          Although their were some differences
                                                                    It took several years, and decades in some
between the results but there correlations have been
                                                          cases, for the computing power to be able to
found acceptable upon comparing their results to
the data obtained from other correlations.                accurately predict the physics in a timely fashion for
          Randall.F.Barron[20],        shows       that   the incredibly small geometries in compact heat
Cryogenic heat exchanger, has showed the effect of        exchangers. That breakthrough allowed for
                                                          significant advancements in the industry.
longitudinal wall heat conduction on the
                                                          Optimization processes were more easily obtained,
performance of cryogenic heat exchangers.
                                                          and more complex geometries could be tested with
Cryogenic heat exchangers operate at low
temperatures where the longitudinal wall heat             the use of CFD.The Fig.6& 7 Shows the CFD
                                                          Analysis in different field Fig.5 show fluid flow in
conduction results in serious performance
deterioration this is because they have small             OSFs geometry and Fig.6 shows that (a) velocity
distances ( on the order of 100 to 200 mm or 4 to 8       field, (b) Velocity distribution, and (c) temperature
                                                          field in OSFs geometry.
in) between the warm and cold ends i.e. they have
short conduction lengths. Because of the natural
requirement of high effectiveness for cryogenic heat
exchangers, the NTU values are usually large (as
high as 500 to 1000), so the effect of longitudinal
conduction is most pronounced for heat exchangers
having short conduction lengths and large NTU. The
wall longitudinal heat conduction reduces the local
temperature difference between the two streams,
thereby reducing the heat exchanger effectiveness
and the heat transfer rate.

6. CFD Analysis
         Heat exchanger designs continued to
expand and develop through the 1960’s and more
industries gained interest in using compact heat          Fig. 7. CFD Analysis in offset plate fins (a)
                                                          Velocity field (b) velocity distribution (c)
exchangers to increase efficiency. Compact heat
                                                          Temperature field
exchanger technologies spread from the automotive
industry to the air conditioning industry, several
manufacturing industries, and even to the magnetic



                                                                                               1310 | P a g e
Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                      Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                       Vol. 3, Issue 1, January -February 2013, pp1306-1312
         In the time since CFD became prevalent in           Flow and Heat transfer in Interrupted Plate
heat exchanger design, several systems of                    passages. International Journal of Heat
commercial codes have been developed to allow for            and Mass Transfer 24:1801-1810
rapid testing and simulations. The programs            3.    Fangjun Hong & Ping Cheng Three
continue to become more accurate, and as                     dimensional numerical analyses and
computers continue to become more powerful and               optimization of offset strip-fin micro-
swift in their calculations, the use of CFD will             channel     heat     sinks     International
expand to new applications.                                  Communications in Heat and Mass
         The technologies available today are leaps          Transfer                    volume36,issue-
and bounds ahead of the resources available to those         7,August2009,Pages 651–656
designing the MSBR in the 1960’s. Computing            4.    Manglik and Bergles A. E. 1995 Heat
power has made hydrodynamics and heat transfer               Transfer and Pressure drop Correlations for
incredibly more accurate in comparison to hand               Rectangular Offset Strip Finn Compact
drawings and manual calculations done in the initial         Heat Exchangers. Experimental Fluid
MSBR design (Bettis, et al., 1967). The computer             Science 10:171-180.
programs developed at ORNL for optimization of         5.     Kays, W. M. and London, A. L. Compact
the heat exchanger designs were rudimentary                  Heat Exchangers, McGraw-Hill, New York
compared to the commercial software packages                 (1984)
available today. Performing CFD analyses in            6.    Hu S and Herold K. E. 1995a Prandtl
FLUENT, with automated optimization available in             Number Effect on Offset Strip Fin Heat
ANSYS Workbench, is much more sophisticated                  Exchanger Performance: Predictive Model
than the analog computer models used in the 1960’s           for Heat Transfer and Pressure Drop.
for overall plant operation (Burke, 1972) and heat           International Journal of Heat and Mass
exchanger design (Bettis, Pickel, Crowley, Simon-            Transfer 38(6) 1043-1051 Hu S and Herold
Tov, Nelms, & Stoddart, 1971).                               K. E. 1995b Prandtl number Effect on
                                                             Offset Strip Fin Heat Exchanger
CONCLUSION                                                   Performance:      Experimental      Results.
         This paper gives a detailed description of          International Journal of Heat and Mass
OSFs types of geometries that can be used to Heat            Transfer 38(6) 1053-1061.
transfer. Offset-strip-fin enhancement geometries      7.    Zhang L. W., Balachandar S., Tafti D. K.
have been developed in order to make heat                    and Najjar F. M. 1997. Heat Transfer
exchangers more efficient and compact. Currently             Enhancement Mechanisms in Inline and
plate-fin heat exchangers are very common in                 Staggered Parallel Plate Fin Heat
cryogenic systems and gas-liquefaction plants.               Exchanger. International Journal of Heat
Increased demand for smaller and better heat                 and Mass Transfer 40(10):2307-2325
exchange devices will certainly lead to more           8.     Dejong N. C., Zhang L. W., Jacobi A. M.,
widespread use of plate-fin heat exchangers in other         Balchandar S. and Tafti D. K.
applications as well.                                        1998.AComplementaryExperimental and
       This review paper discuses the considerable           Numerical Study of Flow and Heat
experimental, Numerical and CFD work which has               Transfer in Offset Strip Fin Heat
been done on heat transfer growth through offset-            Exchangers. Journal of Heat Transfer
strip fin experimental work. There is a need of              12:690:702
analyzing dynamics similarities amongst the            9.    S.YoucefAli_,J.Y.Desmons,Numerical and
geometrical similarities on large scale model                experimental study of a solar equipped
covering industrial application, Further research is         with offset rectangular plate fin absorber
required to be conducted at a large scale on                 plate Volume 31, Issue 13, Pages 2025-
considerable range of curvature ratio, low range of          2206 (October 2006) Renewable Energy an
curvature ratio, low range of Prandtl number and             InternationalJournal,http://www.sciencedir
Reynolds numbers temperature etc.                            ect.com/science/journal/09601481
                                                       10.   Joshi H. M. and Webb R. L. 1987. Heat
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  1.      London, A. L. A Brief History of Compact           Heat Exchanger, International Journal of
          Heat Exchanger Technology, in R. K.                Heat and Mass Transfer. 30(1): 69-80
          Shah, C. F. McDonald and C. P. Howard        11.   Wieting, A. R. Empirical Correlations for
          (Eds),    Compact Heat Exchanger –                 Heat Transfer and Flow Friction
          History, Technological Advancement and             Characteristics of Rectangular Offset-Fin
          Mechanical Design Problems, HTD, 10,               Plate-Fin Heat Exchangers ASME J. Heat
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  2.       Patankar S. V. and Prakash C. 1981 An       12.   Joshi, H. M. and Webb, R. L. Heat
          Analysis of Plate Thickness on Laminar             Transfer and Friction of the Offset Strip-fin



                                                                                         1311 | P a g e
Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and
                 Applications (IJERA) ISSN: 2248-9622 www.ijera.com
                  Vol. 3, Issue 1, January -February 2013, pp1306-1312
      Heat Exchanger Int. J. Heat Mass Transfer
      30(1) 69-84 (1987)
13.   H. Bhowmik and Kwan-Soo 2009.
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14.   Saidi A. and Sudden B. 2001. A Numerical
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      History, Technological Advancement and
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  • 1. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 Offset-Strip Fin Heat Exchangers A Conceptual Review Study ALOK VYAS *, Dr. Alka Bani Agrawal ** *(Department of Mechanical Engineering, Rajeev Gandhi Proudyogiki Vishwavidyalaya, Bhopal (M.P.) – 462038) **(Department of Mechanical Engineering, Rajeev Gandhi Proudyogiki Vishwavidyalaya, Bhopal (M.P.) – 462038) Abstract This paper is a review of research work The geometry of the offset strip fin surface is of last few years on heat transfer growth in described by the following parameters: offset-strip fin heat exchangers. It features a (i) Fin spacing (s), excluding the fin thickness, broad discussion on the application of enhanced (ii) Fin height (h), excluding the fin thickness, heat transfer surfaces to offset strip fin heat (iii) Fin thickness (t), and exchangers. In this paper we are discussing 2D (iv) The strip length (_), in the flow direction. & 3D Analysis in OSF, Experimental & The lateral fin offset is generally uniform investigating research on OSFs, Analytical model and equal to half the fin spacing (including fin to predict the heat transfer coefficient and the thickness). Figure shows a schematic view of the friction factor of the OSFs geometry, Heat rectangular offset strip fin surface and defines the transfer and pressure drop Characteristics of an geometric parameters. The following are some OSFs Thermal performance, CFD Analysis on commonly used secondary parameters derived from OSFs. the basic fin dimensions Keywords - CFD Analysis, Offset-strip fin, Heat transfer growth, laminar and turbulent flow. INTRODUCTION The first sign of movement to relatively “compact” heat exchangers was seen in the automotive industry in the early 1900’s, when an improved manner for removing heat from engines with minimal material (weight) was sought. Whereas heat was previously removed from engines by boiling a collection of water and releasing it into Fig.1Offset-strip fin Geometry the air in an unsophisticated convection process, heat exchangers were seen as an inexpensive way to improve engine performance (Shah & Sekulic, 1. Two & Three Dimensional analysis in 2003).[1] OSFs Heat Exchangers The offset strip fin is one of the most Patankar and Prakash [2] presented a two widely used finned surfaces, particularly in high dimensional analysis for the flow and heat transfer effectiveness heat exchangers employed in in an interrupted plate passage which is an cryogenic and aircraft applications. These fins are idealization of the OSFs heat exchanger. The main created by cutting a set of plain rectangular fins aim of the study is investigating the effect of plate periodically along the flow direction, and shifting thickness in a non-dimensional form t/H on heat each strip thus generated by half the fin spacing transfer and pressure drop in OSF channels because alternately left and rightward. the impingement region resulting from thick plate The flow is thus periodically interrupted, on the leading edge and recalculating region behind leading to creation of fresh boundary layers and the trailing edge are absent if the plate thickness is consequent heat transfer improvement. Interruption neglected. Their calculation method was based on of flow also leads to greater viscous pressure drop, the periodically fully developed flow through one manifested by a higher value of effective friction periodic module since the flow in OSF channels factor. In addition to the effect of wall shear, attains a periodic fully developed behaviour after a resistance to flow also increases due to form drag short entrance region, which may extend to about 5 over the leading edges of the fin sections facing the (at the most 10) ranks of plates (Sparrow, et al. flow, and due to trailing edge vortices. The effective 1977). Steady and laminar flow was assumed by heat transfer coefficient and friction factor are them between Reynolds numbers 100 to 2000. They composite effects of the above mechanisms. found the flow to be mainly laminar in this range, The Offset Strip Fin Geometry although in some cases just before the Reynolds no. 2000 there was a transition from laminar to 1306 | P a g e
  • 2. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 turbulence. Specially for the higher values of t/H. from 10 to 2000 in both the papers. The results of They used the constant heat flow boundary the two studies showed that the Prandtl number has condition with each row of fins at fixed temperature. a significant effect on heat transfer in OSF They made their analysis for different fin thickness channel.Although there is no effect on the pressure ratios t/H= 0, 0.1, 0.2, 0.3 for the same fin length drop. L/H = 1, and they fixed the Prandtl number of fluid Zhang et al [7] investigated the = 0.7. For proper validation they compared there mechanisms for heat transfer enhancement in numerical results with the experimental results of parallel plate fin heat exchangers including the [London and Shah][1] for offset strip fin heat inline and staggered arrays of OSFs. They have also exchangers. The result indicated reasonable taken into account the effect of fin thickness and the agreement for the f factors, but the predicted j factor time dependent flow behavior due to the vortex was twice as large as the experimental data. They shedding by solving the unsteady momentum and concluded that the thick plate situation leads to energy equation. The effects of vortices which are significantly higher pressure drop while the heat generated at the leading edge of the fins and travel transfer does not sufficiently improve despite the downstream along the fin surface was also studied. increased surface area and increased mean velocity. From there study they found that only the surface Fangjun Hong & Ping Cheng [3] show the 3-D interruptions increase the heat transfer because they numerical simulation, taking into consideration the cause the boundary layers to start periodically on fin conjugate heat transfer of heat sink base material surfaces and reduce the thermal resistance to and coolant, was conducted for laminar forced transfer heat between the fin surfaces and fluid. convection of water to study offset strip fin micro However after a critical Reynolds number the flow channel heat sink for microelectronic cooling. It is becomes unsteady and in this regime the vortices found that due to the periodical change of the flow play a major role to increase the heat transfer by direction, the convective heat transfer is enhanced bringing the fresh fluids continuously from the main by mixing the cold and hot coolant, and the stream towards the fin surface. periodical breakup of boundary layer is another Dejong et al [8] carried out an experimental factor to enhance heat transfer. The effects of the and numerical study for understanding the flow and ratio of fin interval to fin length K, and fin numbers heat transfer in OSFs. In the study the pressure drop, M on the performance of strip-fin micro channel local Nusselt number, average heat transfer and skin were also investigated. It is found that for the same friction coefficient on fin surface, instantaneous K, with the increase of M, the required mass flow flow structures and local time averaged velocity rate to keep the maximum wall temperature profiles in OSF channel were investigated. They decreases. compared there results with the experimental results obtained by Dejong and Jacobi [1997] and unsteady 2. Experimental & investigating research on numerical simulation of Zhang et al [1997]. There OSFs results indicate that the boundary layer Manglik and Bergles[4] carried an development, flow separation and reattachment, experimental research on OSFs. They investigated wake formation and vortex shedding play an the effects of fin geometries as non dimensional important role in the OSF geometry. forms on heat transfer and pressure drop, for their S.YoucefAli_,J.Y.Desmons[9] Presented study they used 18 different OSFs. After their A mathematical model that allows the analysis they arrived upon two correlations, one for determination of the thermal performances of the heat transfer and another one for pressure drop. The single pass solar air collector with offset rectangular correlations were developed for all the three regions. plate fin absorber plate is developed (fig.2). The They compared there results from the data obtained model can predict the temperature profile of all the by other researchers in the deep laminar and fully components of the collector and of the air stream in turbulent regions. There correlations can be the channel duct.the offset rectangular plate fins acceptable when comparing the results of the were introduced, which increase the thermal heat expressions to the experimental data obtained by transfer between the absorber plate and the fluid. Kays and London [5]. The offset rectangular plate fins, mounted in a Hu and Herold [6] presented two papers to staggered pattern, are oriented parallel to the fluid show the effect of Prandtl no. on heat transfer and flow and are soldered to the underside of the pressure drop in OSF array. Experimental study was absorber plate. They are characterized by high heat carried out in the first paper to study the effect for transfer area per unit volume and generate the low which they used the seven OSFs having different pressure losses. The experimental results of the air geometries and three working fluids with different stream temperature will be compared with the Prandtl number. At the same time the effect of changing the Prandtl number of fluid with temperature was also investigated. The study was carried out in the range of Reynolds number varying 1307 | P a g e
  • 3. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 results obtained by the theoretical model suggested Fig.3(a) Laminar flow on the fins and in the wakes Fig. 2 Experimental setup (Source Joshi and Webb 1987) The model, which determines the thermal performances of this collector and temperatures of all its components and air stream, uses an equation of global irradiance incident along the collector, ambient and inlet collector temperature. Predicted and experimental results of the air stream temperature are in good agreement particularly in the transition flow regime. On the other hand, in the laminar flow system, the greatest recorded variation, which is of 71ↄC obtained for the lowest value of the Reynolds number Re ¼ 479. In this same case, the difference between the theoretical and the experimental air stream temperature at the collector Fig.3(b) Laminar flow on the fins and oscillating exit is only of 41 ↄC which is acceptable. flow on the wakes (Source Joshi and Webb 1987) 3. Analytical model to predict the heat transfer coefficient and the friction factor of Four different flow regimes were identified the OSFs geometry by Joshi and Webb [12] from their experiment. The Joshi and Webb [10] developed an flow was found to be laminar and steady in the first analytical model to predict the heat transfer regime. In the second regime the oscillating flow coefficient and the friction factor of the offset strip structures were found in the transverse direction. fin surface geometry. To study the transition from The flow oscillated in the wake region between two laminar to turbulent flow they conducted the flow successive fins in the third regime. And in the fourth visualization experiments and an equation based on regime the effect of vortex shedding came into the conditions in wake was developed. They also picture. The laminar flow correlation of Joshi and modified the correlations of Weiting [11]. There Webb started to under predict the j and f factors at was some difference between there correlation. Four the second regime. So they assumed the Reynolds different flow regimes were identified by Joshi and number at that point as the critical Reynolds number Webb [12] from there experiment. The flow was to identify the transition from laminar to turbulent. found to be laminar and steady in the first regime. In the second regime the oscillating flow structures 4. Heat transfer and pressure drop were found in the transverse direction. The flow Characteristics of an OSFs oscillated in the wake region between two H. Bhowmik and Kwan-Soo Lee [13] successive fins in the third regime. And in the fourth studied the heat transfer and pressure drop regime the effect of vortex shedding came into characteristics of an offset strip fin heat exchanger. picture. The laminar flow correlation of Joshi and For their study they used a steady state three Webb started to under predict the j and f factors at dimensional numerical model. They have took water the second regime. So they assumed the Reynolds as the heat transfer medium, and the Reynolds number at that point as the critical Reynolds number number (Re)in the range of 10 to 3500. Variations in to identify the transition from laminar to turbulent. the Fanning friction factor f and the Colburn heat transfer j relative to Reynolds number were observed. General correlations for the f and j factors were derived by them which could be used to analyze fluid flow and heat transfer Characteristics of offset strip fins in the laminar, transition, and turbulent regions of the flow. 1308 | P a g e
  • 4. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 heat transfer coefficient. They also derived the j factor and f factor by using regression analysis. Results showed that the heat transfer coefficient and pressure drop reduce with enlarging the fin space, fin height and fin length. Michna et al [16] investigated the effect of increasing Reynolds number on the performance of OSFs. He conducted the experiment at Reynolds number between 5000 to 120000 and found that both heat transfer and pressure drop increased with increasing Reynolds number, because the effect of vortex shedding and eddy formation at turbulent regime. Operation of OSF heat exchangers under Fig.4 Direction of fluid at LPD & HPD this Reynolds number may be useful in systems where minimizing the heat exchanger size or Saidi and Sudden [14] carried out a maximizing the heat transfer coefficient is more numerical analysis of the instantaneous flow and important than minimizing the pressure drop. heat transfer for OSF geometries in self-sustained Various experiments are carried out in time-dependent oscillatory flow. The effect of order to find out the j and f factors of the various vortices over the fin surfaces on heat transfer was heat exchangers and are called as the thermal studied at intermediate Reynolds numbers where the performance testing. These testing are needed for flow remains laminar, but unsteadiness and vortex heat exchangers, which do not have reported j and f shedding tends to dominate. They compared their data. Therefore, this test is conducted for any new numerical results with previous numerical and development or modification of the finned surfaces. experimental data done by Dejong, et al. (1998). T. Lestina & K. Bell, Advances in Heat Transfer, told for heat exchangers already existing in the plants this test is done for the following reasons: a) Comparison of the measured performance with specification or manufacturing design rating data. b) Evaluation of the cause of degradation or malfunctioning. c) Assessment of process improvements such as those due to enhancement or heat exchanger replacement. Another reason for developing these correlations is that, generally in most heat exchanger problems the working fluid, the heat flow rate and Fig. 5. Heat transfer in offset plate fins mass flow rate are usually known, so if certain correlations between geometry and fin performance The studies of few researchers like is also known, then the problem can be deeply Patankar and Prakash [1], Kays and London [5] it is simplified. For that purpose developing the easy to get information regarding the effects of correlations for fanning friction factor f and OSFs on heat transfer and pressure drop. But most Colbourn factor j are important for heat of the researchers have not taken into account the exchanger.These are the ratio of free flow area ( effect of manufacturing irregularities such as burred = s/h), the ratio of heat transfer area (β= t/l), and the edges, bonding imperfections, separating plate ratio of fin density (y= t/s). roughness which also affect the heat transfer and Show in Fig.1 flow friction characteristics of the heat exchanger. Dong et al [15] made experiments and analysis 5. Thermal performance of OSF Heat considering the above factors to get better thermal Exchangers and hydraulic performance from the OSFs. Sixteen S. Youcef-Ali_, J.Y. Desmons [17] A types of OSFs and flat tube heat exchangers were mathematical model that allows the determination of used to make the experimental studies on heat the thermal performances of the single pass solar air transfer and pressure drop characteristics. A number collector with offset rectangular plate fin absorber of tests were made by changing the various fin plate is developed. The model, which determines the parameters and all the tests were carried out in thermal performances of this collector and specific region of air side Reynolds number (500- temperatures of all its components and air stream, 7500), at a constant water flow crate. The thermal uses an equation of global irradiance incident along performance data was analyzed using the the collector, ambient and inlet collector effectiveness-NTU method in order to obtain the 1309 | P a g e
  • 5. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 temperature. Predicted and experimental results of railway industry (Shah, McDonald, & Howard, the air stream temperature are in good agreement 1980).[21] The 1980’s brought an increase in particularly in the transition flow regime. computing power and function that led compact heat exchanger research away from experimental Suzuki et al [18] in order to study the solutions in favor of Computational Fluid Dynamics thermal performance of a staggered array of vertical (CFD). CFD provided low-cost means to simulate flat plates at low Reynolds number has taken a the physics occurring inside heat exchangers different numerical approach by solving the elliptic relatively accurately, without the need to construct differential equations governing the flow of and test physical apparatus before a final design was momentum and energy. The validation of their developed. numerical model has been done by carrying out experiments on a two dimensional system, followed by those on a practical offset strip fin heat exchanger. The experimental result was in good agreement with the performance study for the practical offset-strip-fin type heat exchanger in the range of Reynolds number of Re<800. Tinaut et al [19] developed two correlations for heat transfer and flow friction coefficients for OSFs and plane parallel plates. The working fluid for OSF was engine oil and water was taken for analyzing the parallel plate channels. By using the correlations of Dittus and Boelter and some expressions of Kays and Crawford they obtained their correlations. For the validation of their results they compared there correlations with correlations of Weitng[6]. Fig. 6. CFD Analysis in offset plate fins Although their were some differences It took several years, and decades in some between the results but there correlations have been cases, for the computing power to be able to found acceptable upon comparing their results to the data obtained from other correlations. accurately predict the physics in a timely fashion for Randall.F.Barron[20], shows that the incredibly small geometries in compact heat Cryogenic heat exchanger, has showed the effect of exchangers. That breakthrough allowed for significant advancements in the industry. longitudinal wall heat conduction on the Optimization processes were more easily obtained, performance of cryogenic heat exchangers. and more complex geometries could be tested with Cryogenic heat exchangers operate at low temperatures where the longitudinal wall heat the use of CFD.The Fig.6& 7 Shows the CFD Analysis in different field Fig.5 show fluid flow in conduction results in serious performance deterioration this is because they have small OSFs geometry and Fig.6 shows that (a) velocity distances ( on the order of 100 to 200 mm or 4 to 8 field, (b) Velocity distribution, and (c) temperature field in OSFs geometry. in) between the warm and cold ends i.e. they have short conduction lengths. Because of the natural requirement of high effectiveness for cryogenic heat exchangers, the NTU values are usually large (as high as 500 to 1000), so the effect of longitudinal conduction is most pronounced for heat exchangers having short conduction lengths and large NTU. The wall longitudinal heat conduction reduces the local temperature difference between the two streams, thereby reducing the heat exchanger effectiveness and the heat transfer rate. 6. CFD Analysis Heat exchanger designs continued to expand and develop through the 1960’s and more industries gained interest in using compact heat Fig. 7. CFD Analysis in offset plate fins (a) Velocity field (b) velocity distribution (c) exchangers to increase efficiency. Compact heat Temperature field exchanger technologies spread from the automotive industry to the air conditioning industry, several manufacturing industries, and even to the magnetic 1310 | P a g e
  • 6. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 In the time since CFD became prevalent in Flow and Heat transfer in Interrupted Plate heat exchanger design, several systems of passages. International Journal of Heat commercial codes have been developed to allow for and Mass Transfer 24:1801-1810 rapid testing and simulations. The programs 3. Fangjun Hong & Ping Cheng Three continue to become more accurate, and as dimensional numerical analyses and computers continue to become more powerful and optimization of offset strip-fin micro- swift in their calculations, the use of CFD will channel heat sinks International expand to new applications. Communications in Heat and Mass The technologies available today are leaps Transfer volume36,issue- and bounds ahead of the resources available to those 7,August2009,Pages 651–656 designing the MSBR in the 1960’s. Computing 4. Manglik and Bergles A. E. 1995 Heat power has made hydrodynamics and heat transfer Transfer and Pressure drop Correlations for incredibly more accurate in comparison to hand Rectangular Offset Strip Finn Compact drawings and manual calculations done in the initial Heat Exchangers. Experimental Fluid MSBR design (Bettis, et al., 1967). The computer Science 10:171-180. programs developed at ORNL for optimization of 5. Kays, W. M. and London, A. L. Compact the heat exchanger designs were rudimentary Heat Exchangers, McGraw-Hill, New York compared to the commercial software packages (1984) available today. Performing CFD analyses in 6. Hu S and Herold K. E. 1995a Prandtl FLUENT, with automated optimization available in Number Effect on Offset Strip Fin Heat ANSYS Workbench, is much more sophisticated Exchanger Performance: Predictive Model than the analog computer models used in the 1960’s for Heat Transfer and Pressure Drop. for overall plant operation (Burke, 1972) and heat International Journal of Heat and Mass exchanger design (Bettis, Pickel, Crowley, Simon- Transfer 38(6) 1043-1051 Hu S and Herold Tov, Nelms, & Stoddart, 1971). K. E. 1995b Prandtl number Effect on Offset Strip Fin Heat Exchanger CONCLUSION Performance: Experimental Results. This paper gives a detailed description of International Journal of Heat and Mass OSFs types of geometries that can be used to Heat Transfer 38(6) 1053-1061. transfer. Offset-strip-fin enhancement geometries 7. Zhang L. W., Balachandar S., Tafti D. K. have been developed in order to make heat and Najjar F. M. 1997. Heat Transfer exchangers more efficient and compact. Currently Enhancement Mechanisms in Inline and plate-fin heat exchangers are very common in Staggered Parallel Plate Fin Heat cryogenic systems and gas-liquefaction plants. Exchanger. International Journal of Heat Increased demand for smaller and better heat and Mass Transfer 40(10):2307-2325 exchange devices will certainly lead to more 8. Dejong N. C., Zhang L. W., Jacobi A. M., widespread use of plate-fin heat exchangers in other Balchandar S. and Tafti D. K. applications as well. 1998.AComplementaryExperimental and This review paper discuses the considerable Numerical Study of Flow and Heat experimental, Numerical and CFD work which has Transfer in Offset Strip Fin Heat been done on heat transfer growth through offset- Exchangers. Journal of Heat Transfer strip fin experimental work. There is a need of 12:690:702 analyzing dynamics similarities amongst the 9. S.YoucefAli_,J.Y.Desmons,Numerical and geometrical similarities on large scale model experimental study of a solar equipped covering industrial application, Further research is with offset rectangular plate fin absorber required to be conducted at a large scale on plate Volume 31, Issue 13, Pages 2025- considerable range of curvature ratio, low range of 2206 (October 2006) Renewable Energy an curvature ratio, low range of Prandtl number and InternationalJournal,http://www.sciencedir Reynolds numbers temperature etc. ect.com/science/journal/09601481 10. Joshi H. M. and Webb R. L. 1987. Heat REFERENCES Transfer and Friction in Offset Strip Fin 1. London, A. L. A Brief History of Compact Heat Exchanger, International Journal of Heat Exchanger Technology, in R. K. Heat and Mass Transfer. 30(1): 69-80 Shah, C. F. McDonald and C. P. Howard 11. Wieting, A. R. Empirical Correlations for (Eds), Compact Heat Exchanger – Heat Transfer and Flow Friction History, Technological Advancement and Characteristics of Rectangular Offset-Fin Mechanical Design Problems, HTD, 10, Plate-Fin Heat Exchangers ASME J. Heat ASME, 1-4, (1980) Transfer 97 488-490 (1975) 2. Patankar S. V. and Prakash C. 1981 An 12. Joshi, H. M. and Webb, R. L. Heat Analysis of Plate Thickness on Laminar Transfer and Friction of the Offset Strip-fin 1311 | P a g e
  • 7. Alok Vyas, Dr. Alka Bani Agrawal / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp1306-1312 Heat Exchanger Int. J. Heat Mass Transfer 30(1) 69-84 (1987) 13. H. Bhowmik and Kwan-Soo 2009. Analysis of Heat Transfer and Pressure DropCharacteristics in an Offset Strip Fin Heat Exchanger. International Journal of Heat and MassTransfer 259-263 14. Saidi A. and Sudden B. 2001. A Numerical Investigation of Heat Transfer Enhancement in Offset Strip Fin Heat Exchangers in Self Sustained Oscillatory Flow. International Journal of Numerical Methods for Heat and Fluid Flow. 11(7): 699-716 15. Dong J., Chen J., Chen Z. and Zhou Y. 2007. Air Side Thermal hydraulic Performance of Offset Strip Fin Heat Exchangers Fin Alumunium Heat Exchangers. Applied Thermal Engineering 27:306-313 16. Michna J. G., Jacobi A. M. and Burton L. R. 2005. Air Side Thermal- Hydraulic Performance of an Offset Strip Fin Array at Reynolds Number up to 12, 0000. Fifth International Conference on Enhanced Compact and Ultra Compact Heat Exchangers. Science, Engineering and Technology 8-14. 17. S. Youcef-Ali_, J.Y. Desmons Numerical and experimental study of a solar equipped with offset rectangular plate fin absorber plate Volume 31, Issue 13, Pages 2025- 2206 (October 2006) Renewable EnergyanInternationalJournal,http://www. sciencedirect.com/science/journal/0960148 1 18. Suzuki, K., Hiral, E., Miyake, T., Numerical and Experimental studies on a two Dimensional Model of an Offset-Strip- Fin type Compact Heat Exchanger used at low Reynolds Number. International Journal of Heat and Mass Transfer 1985 28(4) 823-836 19. Tinaut F. V., Melgar A. and Rehman Ali A. A. 1992 Correlations for Heat Transfer and Flow Friction Characteristics of Compact Plate Type Heat Exchangers. International Journal of Heat and Mass Transfer. 35(7):1659:166 20. Barron R. F., Cryogenic Heat Transfer, Taylor and Francis (1999) 311-318. 21. R. K. Shah, C. F. McDonald and C. P. Howard (Eds), Compact Heat Exchanger – History, Technological Advancement and Mechanical Design Problems, HTD, 10, ASME, 1-4, (1980) 1312 | P a g e